For addition, drag tiles onto the board,

A study of long-distance phone calls made from General Electric's corporate headquarters in Fairfield, Connecticut, revealed the

Jet001 [13]

Answer:

a) 0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

b) 0.0668 = 6.68% of the calls last more than 4.2 minutes

c) 0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

d) 0.9330 = 93.30% of the calls last between 3 and 5 minutes

e) They last at least 4.3 minutes

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 3.6, \sigma = 0.4$

(a) What fraction of the calls last between 3.6 and 4.2 minutes?

This is the pvalue of Z when X = 4.2 subtracted by the pvalue of Z when X = 3.6.

X = 4.2

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4.2 - 3.6}{0.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

X = 3.6

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3.6 - 3.6}{0.4}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5

0.9332 - 0.5 = 0.4332

0.4332 = 43.32% of the calls last between 3.6 and 4.2 minutes

(b) What fraction of the calls last more than 4.2 minutes?

This is 1 subtracted by the pvalue of Z when X = 4.2. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4.2 - 3.6}{0.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

1 - 0.9332 = 0.0668

0.0668 = 6.68% of the calls last more than 4.2 minutes

(c) What fraction of the calls last between 4.2 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 4.2. So

X = 5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5 - 3.6}{0.4}$

$Z = 3.5$

$Z = 3.5$ has a pvalue of 0.9998

X = 4.2

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{4.2 - 3.6}{0.4}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

0.9998 - 0.9332 = 0.0666

0.0666 = 6.66% of the calls last between 4.2 and 5 minutes

(d) What fraction of the calls last between 3 and 5 minutes?

This is the pvalue of Z when X = 5 subtracted by the pvalue of Z when X = 3.

X = 5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5 - 3.6}{0.4}$

$Z = 3.5$

$Z = 3.5$ has a pvalue of 0.9998

X = 3

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{3 - 3.6}{0.4}$

$Z = -1.5$

$Z = -1.5$ has a pvalue of 0.0668

0.9998 - 0.0668 = 0.9330

0.9330 = 93.30% of the calls last between 3 and 5 minutes

(e) As part of her report to the president, the director of communications would like to report the length of the longest (in duration) 4% of the calls. What is this time?

At least X minutes

X is the 100-4 = 96th percentile, which is found when Z has a pvalue of 0.96. So X when Z = 1.75.

$Z = \frac{X - \mu}{\sigma}$

$1.75 = \frac{X - 3.6}{0.4}$

$X - 3.6 = 0.4*1.75$

$X = 4.3$

They last at least 4.3 minutes

7 0

3 years ago

At the rate of $2.00 per square foot the cost of painting the rectangular board with a semicircular top shown in the figure is $

Elenna [48]

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.
<span>
it consists of a rectangle, dimensions L = 4ft and W = 3ft = Ar = 4ft x 3ft = 12 ft^2

</span>then, you have one half of the area of the circle that has diameter R = 3ft - radius will be r = 1.5ft the area of that half will be:

Ac = r^2 $\pi$ / 2
= (1.5 ft)^2 x 3.14 / 2
= 2.25 ft^2 x 3.4/2
= 7.065 ft^2/ 2
= 3.5325ft^2

A = Ar + Ac
A = 12ft^2 + 3.5325ft^2
A = 15.5325ft^2

<span>At the rate of $2 per square foot, the cost will be:
$ 15.5325*2 = 31.07 </span>

5 0

3 years ago

Read 2 more answers

A 6th grade student can complete 20 multiplication facts in 1 minute. If he works at the same rate how long should it take him t

Usimov [2.4K]

He can complete 35 questions in 1.75 minutes

1/20=x/35
Simplify both sides
x=1.75

7 0

3 years ago

Read 2 more answers

How to change the expression to a single logarithm

IrinaK [193]

First, you'll use the "Log power rule," which says that $\log_ax^p=p\log_ax$ . In this case, you're going from the form on the right (with p in front of the log) to the form on the left (with p in the exponent position). So, the expression becomes:

$\log_7x^4+\log_7y^8+\log_7z^4$

Then, you'll use the "Log product rule," which says that $\log_a(xy)=\log_ax+\log_ay$ . Again, you're going from the form on the right to the form on the left (basically, from the sum of the logs, to a log of the products). So you get:

$\log_7(x^4y^8z^4)$

There's your expression simplified into a simple logarithm.

6 0

3 years ago

Write the equation of a horizontal line that passes through the point (–2, 2).

Aneli [31]

Answer:

option C

y = 2

Step-by-step explanation:

Given in the question,

a co-ordinate = (-2,2)

x = -2

y = 2

Equation of the straight line

y = mx + c

<em>here m = gradient of the line</em>

<em> c = y - intercept</em>

<em />

<h3>we know that gradient of the horizontal line = 0</h3>

plug value in the equation above

y = (0)x + 2

y = 2

7 0

3 years ago